A screw injecting apparatus includes a check valve mounted on the tip end portion of a screw and adapted to be opened and closed in response to rotation of the screw, and a control for controlling operation of the screw such that in a metering phase of molding process, the screw rotates in one direction to feed a melt of molding material toward the nozzle while the check valve is in an open state, when a metered amount of melt is accumulated forward of the tip end portion, the screw moves backward by a predetermined distance to reduce a reaction from the melt accumulated around the tip end portion, thereafter, the screw rotates in the reverse direction to close the check valve and cause the screw to advance until the amount of forward movement of the screw becomes substantially equal to the predetermined distance of backward movement achieved previously.